Geometric Deformations of Discriminants and Apparent Contours
暫譯: 判別式的幾何變形與表面輪廓

本書呈現了在歐幾里得三維空間中，表面明顯輪廓的變形及平面對平面映射微分的全新原創結果。給定一個觀察方向，明顯輪廓（也稱為輪廓或外形）是表面上觀察方向與表面相切的點集的投影。明顯輪廓在計算機視覺和圖像分析中被廣泛使用，並且帶來了重大的數學挑戰。

隨著觀察方向的變化，明顯輪廓會變形，出現和消失的拐點和頂點。本書提供了這些分岔的完整目錄，針對一般表面隨著觀察方向的變化。此外，還探討了幾何不變量，這些不變量決定了在明顯輪廓的變形中可能出現的最大拐點和頂點數量。本書旨在為從事微分幾何、奇異性理論、計算機視覺及相關領域的研究人員提供參考資料，同時也可作為本科生閱讀課程的教材。

Farid Tari is a Full Professor at the University of São Paulo. He has published over 60 research papers, including some in leading mathematical journals, authored one book, and edited another. He has supervised several postdoctoral fellows, PhD, and MSc students. Currently, he serves as an Associate Editor of the Journal of Singularities.

Mostafa Salarinoghabi is currently a postdoctoral researcher at the Federal University of Viçosa, Brazil. He earned his PhD from the University of São Paulo, Brazil. His expertise lies in differential geometry, singularity theory, and random complex dynamics.

Masaru Hasegawa is currently an Assistant Professor at Iwate Medical University, Japan. He earned his PhD from Saitama University, Japan, where he also held a postdoctoral position. Additionally, he completed another postdoctoral position at the University of São Paulo, Brazil. His research focuses on applying singularity theory to differential geometry.

法里德·塔里是聖保羅大學的全職教授。他已發表超過60篇研究論文，包括一些在領先的數學期刊上，並著作一本書，編輯另一本書。他指導過多位博士後研究員、博士及碩士生。目前，他擔任《奇異性期刊》的副編輯。

莫斯塔法·薩拉里諾哈比目前是巴西維索薩聯邦大學的博士後研究員。他在巴西聖保羅大學獲得博士學位。他的專長在於微分幾何、奇異性理論和隨機複雜動力學。

長谷川勝目前是日本岩手醫科大學的助理教授。他在日本埼玉大學獲得博士學位，並在該校擔任過博士後職位。此外，他還在巴西聖保羅大學完成了另一個博士後職位。他的研究重點是將奇異性理論應用於微分幾何。